Question

(Round answers to
the nearest hundredth.)

Answer 1

28.31

Explanation:

So in this case you're going to need to use the law of sines which essentially states that:
`(a)/(sinA)=(b)/(sinB)` which should apply to any of the sides. the lowercase a and b are the opposite sides of the angles A and B. In this example the angle A is given and C is given, but not in the text. Since you have the right angle thing in the diagram, angle C is a right angle (90 degrees).

Given information:

`\angle A = 32\\a=15\\\angle C = 90 \text{(the right angle symbol in the diagram of the triangle)}`

Law of sines equation:

`(a)/(sinA)=(b)/(sinB) \text{ can be applied to any two sides }`

Plug in known information:

`(15)/(sin(32))=(c)/(sin (90))`

since sin(90) = 1, simplify the fraction

`(15)/(sin(32)) = c`

Calculate sin(32)

`(15)/(0.530)\approx c`

Divide

`28.306\approx c`

If you haven't learned law of sines yet and don't quite understand why it works you can also use the definition of tan to find what b equals and then use the Pythagorean Theorem to solve for c

tan is defined as:
`(opposite)/(adjacent)`

`tan(32)=(15)/(b)`

now multiply both sides by b

`b * tan(32)=15`

Divide both sides by tan 32

`b = (15)/(tan(32))`

`b\approx 24.005`

Now use the Pythagorean Theorem:
`a^2+b^2=c^2`

`(24.005)^2+15^2=c^2\\`

Square known values

`576.241+225=c^2`

Add the values

`801.241 = c^2`

take the square root of both sides

`28.306\approx c`

Rounding to the nearest hundredth gives you 28.31